I'm not sure I understand completely. I'd figure that using a smaller gear ratio would make a plane faster when comparing like props and motors. Here's my logic.
Let's say we use you above example for a motor. I know there's going to be a discrepency for added weight as far as RPM's are concerned (or would it just cause it to draw more amps?). It's moving 31500 RPM with no prop. You put it on a gear box #1 (6:1). It will turn the propeller gear at 5250 RPM. Now we put it on gearbox #2 (3:1). This turns the prop at 10500 RPM. If you put the same prop on both gearboxes, wouldn't the second one be a faster plane?
And is there a difference between speed and power? I was thinking that if a setup had more power, then it has more speed. That the gearbox acted like a sort of governer to make sure it didn't go too fast.
And also a thing or two about prop size. There has to be a third number or factor when dealing with props. Otherwise, there's no difference between an 8-4 prop and a 5-4 prop. They both have a pitch of 4 and as stated earlier
Pitch is the theoretical distance the prop would move forward in an ideal fluid under ideal conditions.
I can only think that the greater the diameter, the more air it has to cut through which makes it draw more amps but allows it to push/pull harder as well. Which means that the two props on identical planes wouldn't follow the "rule of pitch (or whatever)" that I posted above. Or I just have no idea what "ideal conditions" really are. The only thing that I can think of for a third number is weight and/or air resistance.